In practice, it is not uncommon to have access to only a few ports on a server. If that is the case, the database port is probably not one of them. However, you can still connect to the database as long as you have SSH access to the server. To do this, you need to set up an SSH tunnel.
Using SSH with Git on Windows mostly works out of the box. The .gitignore file allows a lot of additional configuration. The sshCommand in the core section allows you to specify the path and arguments for the ssh.exe command. However, specifying a path there is mostly asking for trouble.
Although Git can be used over HTTPS with username and password authentication, it's much more convenient to use over SSH. Now that OpenSSH client is included in Windows 10, SSH can be easily set up without any third-party clients.
In Windows, there are two approaches to accessing Git repositories using SSH. Command line Git distribution and posh-git are preconfigured for OpenSSH, while SourceTree by default relies on PuTTY. The two stacks use different formats for storing both private and public keys. Fortunately, there is a way to convert between the formats using PuTTY's key generation utility.